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Answer :
Final answer:
(a) the correct answer. The final isotope produced in the thorium decay series, where thorium-232 loses six alpha particles and four beta particles, is lead-208. This is because the final atomic mass will be 208, and the atomic number will be 82, corresponding to the element lead (Pb).
Explanation:
In the thorium decay series, thorium-232 undergoes a sequence of radioactive decays, which includes the emission of six alpha particles and four beta particles. Each alpha particle emitted results in a decrease of the atomic mass by 4 units and the atomic number by 2 units, whereas each beta particle emitted results in an increase of the atomic number by 1 unit without changing the atomic mass.
Starting with thorium-232 (atomic number 90, mass number 232), after losing six alpha particles (6 × 4 = 24 mass units; 6 × 2 = 12 atomic number units) and four beta particles （which do not affect the mass number but increase the atomic number by 4), the final isotope reaches a mass number of 208 (232 - 24) and an atomic number of 82 (90 - 12 + 4). The element with atomic number 82 is lead (Pb), so the stable isotope produced at the end of the decay series is lead-208 (Pb-208).
Therefore, the final isotope produced in the thorium decay series is lead-208, which makes option (a) the correct answer.
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